If two zeroes of the polynomial x³ + x² − 9x − 9 are 3 and −3, find its third zero

Video Explanation

Watch the video explanation below:

Given

f(x) = x³ + x² − 9x − 9

Two zeroes of the polynomial are:

3 and −3

To Find

The third zero of the polynomial.

Solution

Let the third zero be α.

For a cubic polynomial:

Sum of zeroes = −(coefficient of x²)/(coefficient of x³)

= −1/1 = −1

Step 1: Use the Sum of Zeroes

3 + (−3) + α = −1

0 + α = −1

α = −1

Final Answer

The third zero of the polynomial is:

−1

Correct Option

(a) −1

Conclusion

Hence, if two zeroes of the polynomial x³ + x² − 9x − 9 are 3 and −3, then its third zero is −1.